Supplementary difference sets and optimal designs

D-optimal designs of order n = 2v ≡ 2 (mod 4), where q is a prime power and v = q2 + q + 1 are constructed using two methods, one with supplementary difference sets and the other using projective planes more directly. An infinite family of Hadamard matrices of order n = 4v with maximum excess (n) = n√n - 3 where q is a prime power and v = q2 + q + 1 is a prime, is also constructed.